Many physiological processes in cell membranes require lateral diffusion: transport by mobile redox carriers ill mitochondria and chloroplasts, diffusion-coupled activation of G-protein by rhodopsin in rod outer segments, aggregation of mobile receptors for hormones and antibodies. Lateral diffusion is hindered by high concentrations of mobile species, or by the presence of immobile species such as gel-phase lipid domains or immobilized proteins. In this project, the effect of obstacles on diffusion and diffusion-mediated reactions will be analyzed by means of percolation theory and Monte Carlo calculations. The use of lateral diffusion measurements as a probe of submicroscopic domain structure in cell membranes will be modeled, including the effect of lipid domains on diffusion, and measurements of motion of individual particles on the cell surface at nanometer resolution. In many types of cells, the restriction of lateral diffusion of plasma membrane proteins is essential to differentiation. One means of accomplishing this is the membrane skeleton. The spectrin network attached to the erythrocyte plasma membrane is the best-known example, but similar networks are found in other cells, such as epithelial and nerve cells. The membrane skeleton obstructs lateral diffusion and provides mechanical reinforcement to the plasma membrane. This project will continue the development of a unified model of these effects, showing how the integrity of the network affects the diffusion coefficient of membrane proteins, and the elasticity and mechanical stability of the membrane skeleton. The emphasis will be on a model of the breakdown of the membrane skeleton under mechanical stress, to find the probability that a defective membrane skeleton will break down under a given stress, and to characterize gaps in the network where membrane may be lost by vesiculation. The breakdown model will be extended to include the effects of a toughening mechanism and variation in protein- protein binding constants. The results will show the effects of missing, defective, or oxidized spectrin, as in hereditary hemolytic anemia, sickle cell anemia, and stored blood. The model will be further extended to three dimensions to examine the consequences of damage to the cytoskeleton in a wide variety of disorders.